Phase behavior of large three-dimensional (3D) complex plasma systems under microgravity conditions onboard the International Space Station is investigated. The neutral gas pressure is used as a control parameter to trigger phase changes. Detailed analysis of structural properties and evaluation of three different melting-freezing indicators reveal that complex plasmas can exhibit melting by increasing the gas pressure. Theoretical estimates of complex plasma parameters allow us to identify main factors responsible for the observed behavior. The location of phase states of the investigated systems on a relevant equilibrium phase diagram is estimated. Important differences between the melting process of 3D complex plasmas under microgravity conditions and that of flat 2D complex plasma crystals in ground based experiments are discussed.